Radomes are usually constructed from sandwich structures made of materials which usually have a low dielectric constant so that they do not interfere with electromagnetic waves. Performance of the antenna is increased by the appropriate assortment of materials enabling it to survive under marine applications, and it depends on composite strength-to-weight ratio, stiffness, and resistance to corrosion. The design of a sandwich core submarine radome greatly depends on the material system, number of layers, orientation angles, and thickness of the core material. In this paper, a conceptual design study for a sandwich core submarine radome is carried out with the help of finite element analysis (FEA) using two unidirectional composite materials—glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP)—as a skin material and six different core materials. Conceptual designs are obtained based on constraints on the composite materials’ failure, buckling, and strength. The thickness of the core is reduced under constraints on material and buckling strength. Finite element analysis software ANSYS WORKBENCH is used to carry out all the simulations.